Pathway XIV

ℂComplex analysis

i as a quarter-turn, multiplication as rotate-and-scale, Euler's identity, poles.

1. 01What i isThe number i is a quarter-turn. Multiplying by i twice is −1.4 min
2. 02Multiply by rotatingTo multiply complex numbers: multiply lengths, add angles.5 min
3. 03Euler's formulae^{iθ} walks the unit circle. At π it lands on −1.5 min
4. 04Poles and meromorphic functionsA meromorphic function is holomorphic except for isolated poles — infinities of finite order.5 min